Inverse scattering on the line for the nonlinear Klein-Gordon equation with a potential

[摘要] In this paper we obtain a L-p - L-p' estimate for the Klein-Gordon equation with a potential on the fine. This result follows from the previously known estimates in the case without potential and from the continuity on the Sobolev spaces of the Schrodinger wave operators that we proved in a previous paper. Using this estimate we construct the scattering operator for the nonlinear Klein-Gordon equation with a potential. Moreover, we prove that the small amplitude scattering operator uniquely determines both the potential and the nonlinearity. Our proof also gives a method for the reconstruction of the potential and of the nonlinearity. (C) 2000 Academic Press.

[发布日期] 2000-12-01